The ability to culture complex organs is currently an important goal in biomedical research. It is possible to grow organoids (3D organ-like structures) in vitro; however, a major limitation of organoids, and other 3D culture systems, is the lack of a vascular network. Protocols developed for establishing in vitro vascular networks typically use human or rodent cells. A major technical challenge is the culture of functional (perfused) networks. In this rapidly advancing field, some microfluidic devices are now getting close to the goal of an artificially perfused vascular network. Another development is the emergence of the zebrafish as a complementary model to mammals. In this review, we discuss the culture of endothelial cells and vascular networks from mammalian cells, and examine the prospects for using zebrafish cells for this objective. We also look into the future and consider how vascular networks in vitro might be successfully perfused using microfluidic technology.